1. Field of the Invention
This invention relates to a function generator, more particularly to a function generator whose output attains or reaches to a desired value at a designed definite time and in which, the desired value and/or the time can be varied in the course of attainment as desired.
2. Description of the Prior Art
Function generators which generate outputs of prescribed functions in response to inputs have been well-known. One example is taught by Japanese Patent Publication No. 56(1981)-44451. The function generator taught there includes an integrator and generates an output of a ramp function varying linearly with respect to time.
It should be noted, however, that the term "function generator" is used in this specification to not only mean the so-called function generator such as taught by the above reference, but also to include any computing means which generates a value a specific function as desired. In that broader sense, a technique proposed by Japanese Laid-open Patent Publication No. 3(1991)-245201 can further be cited as a prior art. This discloses a control system for a robot or the like involving some limitations .such as a voltage to be supplied to the robot's motor being restricted to a predetermined value. The system generates a control input which enables an output (controlled variable) to be in coincident with a desired value within a possible shortest time.
Aside from the above, when generating a trajectory of a robot such as a trajectory of a free (swing) leg of a legged mobile robot, the trajectory has to be generated taking into account the restriction on the free (swing) leg's footfall time. Because of this, there is a need for a function generator able to produce an output which varies smoothly from an initial value to a desired value and to complete the transition to the desired value at a designated definite attainment time. This can not be satisfied by the techniques proposed in the aforesaid references. In addition, there is a need for a function generator with this capability which is further capable of changing the desired value or the designated attainment time in the course of the transition.
If one attempts to constitute the function generator using a filter, particularly using one of the various types of digital filters that have become available in recent years, one has a choice between the two general categories of digital filters: the FIR or non-recursive digital filter and the IIR or recursive digital filter. Each of these has its drawbacks. Although the FIR digital filter has a finite settling time and can smoothly correct its output when the desired value is changed in the course of attainment, it does not allow the settling time (designated attainment time) to be changed. Moreover, when designed to have a long settling time, the filter involves a high-order linear difference equations with constant difference quotients which greatly increase the amount of computation. Although the IIR digital filter can smoothly correct its output when the desired value is changed in the course of attainment and does not involve a large amount of computation, it does not allow the settling time to be changed and does not have a finite settling time. These same shortcomings are also encountered with the use of analogue filters. While it is conceivable not to use a filter but instead to use a polynomial expression for obtaining the desired output, this also runs into the problem high-volume computation and a very high degree of difficulty in changing the desired value or designated attainment time in the course of attainment.